Geodesic
Local rigidity of partially hyperbolic actions I. KAM method and ${\mathbb Z^k}$ actions on the torus
Danijela Damjanović1 ; Anatole Katok2
1Department of Mathematics<br/>Rice University, 6100 Main Street, Houston, TX 77005<br/>United States
2Department of Mathematics<br/>The Pennsylvania State University<br/>University Park<br/>State College, 16802<br/>United States
Annals of mathematics, Tome 172 (2010) no. 3, pp. 1805-1858
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We show $\Bbb C^\infty$ local rigidity for $\mathbb{Z}^k$ $(k\ge 2)$ higher rank partially hyperbolic actions by toral automorphisms, using a generalization of the KAM (Kolmogorov-Arnold-Moser) iterative scheme. We also prove the existence of irreducible genuinely partially hyperbolic higher rank actions on any torus $\mathbb{T}^N$ for any even $N\ge 6$.

DOI : 10.4007/annals.2010.172.1805

Danijela Damjanović   1   ; Anatole Katok  2

1 Department of Mathematics<br/>Rice University, 6100 Main Street, Houston, TX 77005<br/>United States
2 Department of Mathematics<br/>The Pennsylvania State University<br/>University Park<br/>State College, 16802<br/>United States 
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     title = {Local rigidity of partially hyperbolic actions {I.} {KAM} method and ${\mathbb Z^k}$ actions on the torus},
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Danijela Damjanović ; Anatole Katok. Local rigidity of partially hyperbolic actions I. KAM method and ${\mathbb Z^k}$ actions on the torus. Annals of mathematics, Tome 172 (2010) no. 3, pp. 1805-1858. doi: 10.4007/annals.2010.172.1805

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